When it comes to investing, people are always looking for the best method, but there is a French proverb: the best, the enemy of the good. As we carefully reviewed our experience over the past few years, we found that this proverb seemed to state some facts: we once believed in blue chips, value stocks, and also briefly envied racetrack stocks. In the last few years before the Spring Festival, the market was still chasing small micro cap stocks, and all of them experienced bombings without exception. The latest belief is high dividend stocks, but blue chips, value stocks, and high-dividend stocks have a strong correlation, so after going around a circle, our beliefs seem to have returned to their original place, only to reappear with different narratives and different names.
It seems that the investment problem is not a stock selection issue, but rather a matter of choosing the timing, specifically: entering early when the advantage categories rise, then exiting and entering the next advantage category at the beginning of the decline in these categories. This means that we need a magic crystal ball that can accurately predict every step of the way. However, there is no magic crystal ball, because according to the law of deduction, if it exists, it will become an obvious study, and the market will have a long-lasting winner. This means that this small ecosystem, which continues to expand, will one day surpass the entire ecosystem (currency) and replace it. We have never discovered the two in practice, and logically impossible to occur. Therefore, this assumption must be wrong. If you want to solve the root problem at the right time, it is still a false problem.
For a long time, we have relied on so-called corroborating evidence that has already occurred, yet the truth is that subsequent facts keep punching us in the face. why? The apparent observation is that people may be able to be perfect when entering, but no matter what, they cannot exit in a timely manner. Even with AI support, tail risks always come suddenly, which is surprising, and even if you can find the direct cause (for example, the systemic decline before the holiday season can be attributed to the relevant investors' bottom-up contract risk, that is, the risk of having to trade), it is impossible to prevent it in advance. I think the root cause is: historical evidence has not been tested by high-level reactions; only tests that simulate what has happened can represent the future.
However, we must be convinced that the best need not be enemies of the good. Otherwise, this means true defeatism and nihilism — our historical track record exists only on the path of luck. We have always been fooled by randomness, unable to overcome luck, only at the mercy of fate, and our past work experience has become meaningless.
Naturally, it is impossible to act without rules. So are there really any good people? I think it is, but it's far from being as simple and straightforward as a specific plan. There are two main causes of cognitive problems: part of the factor is that people always have limited attention and can only focus on the explicit part; more importantly, the truth is hidden and never revealed. Questions and answers are always in opposition. Admittedly, an established question does have the most reasonable answer, but wouldn't an established answer have a question attacking and denying it through high-level responses? Of course there are! Therefore, what is needed is a comparative standard hidden behind a specific plan, or called relative truth, which can only be interpreted through falsification laws.
Read the book a hundred times; the meaning is self-evident. After reading “Safe Haven” many times, my understanding of the author's statement (although it is also a guess) continues to improve. Here, I will use the illustrated method in the book to show this relative truth, but first keep in mind my summary of these figures: same benchmark, verify one by one.
The so-called same benchmark means that the test must be carried out in the same time and space. For the same target, we also need to use the same comparison benchmark: locked geometric average yield, same risk level, same median fraction (50% quantile) or safety quantile (5% quantile). Any inspection that violates this regulation is not strict. What effect would this lack of rigor have? Research that starts from realistic evidence will always have differences in sampling from survivors' evidence. Fundamentally speaking, it is a comparison of two different things, but the result is that there is no obvious difference between these different things. The result is that no one comes first, or we are not convinced about the research results, and it is naturally even less reliable to use solutions that we are not convinced of; or we take it lightly, and this is a retrospective mistake. In the end, we use this as a standard to guide subsequent actions, commit forward-looking mistakes, and eventually become disillusioned in the higher order of beliefs about things. Malignancy that has always occurred in reality cycle.
Verification one by one allows us to slow down and verify one by one, rather than rashly believing in intuitive judgment. In fact, after verifying one by one, you will always find very important counterintuitive facts. Verification one by one does not occur in reality, but simulates all paths, thus eliminating sampling bias.
In terms of the testing procedure, we adopted the physicist Professor Feynman's suggestion: first, make a guess. Then, calculate the results of the guess and find out what it means if the guess is correct. Next, compare the calculation results directly with the observations to see if it works. If it's inconsistent with the experiment, it's wrong.
Guessing stage
The rigorous and sophisticated experimental design was inspired by the philosophers' ideas, starting with Bernoulli. Bernoulli's contribution is the Bernoulli waterfall chart (logarithmic chart) presented below. The reason for using a logarithmic graph is because there is a formal relationship between the logarithmic graph and the geometric average yield, and the geometric average yield is a real reality (definitely not an arithmetic average yield), and the geometric average yield can be replaced by an approximation of the median of the sequence.
The point of the Bernoulli Waterfall chart is to try to avoid major losses, because significant losses can cause disproportionately significant damage to the geometric average return. Compound interest is the atomic bomb in economics, but it is also a double-edged sword. People only project their limited attention on significant positive data, and there is almost no protection against the other side of the double-edged sword. People seem to forget: only by not killing me can make me stronger. Before you become powerful, you must check and confirm whether the methodology you believe in will kill you.
The above chart tells us that when the logarithmic curve is a little below y = 1, we are facing the tipping point of Bernoulli Falls. On the left side of the tipping point, there are actually only statistically significant values and solid lines. In reality, this means that the assets under management have fallen into a state of no avail. They may have died out or are struggling to death, and will eventually become silent evidence. To avoid this concave curve, you need a highly convex curve force to balance.
Since the risk of explosion usually occurs at the tail end of a particular asset, we also call it tail risk. To show the tail, we slightly deformed it and mirrored the right side of the above two images, that is, the beginning is on the left and the tail is on the right. The benefits at each time point of the two graphs are then combined. The process of compounding is the process of adding and subtracting the benefits at each stage, then multiplying and opening the square root. How many times are compounded and how many times to square the root. After fitting in this way, it is basically a straight line with a leveled slope close to the X axis. It usually falls into the first quadrant. The slope represents the geometric yield up to the present in time. The number may be small; the important thing is that it actually exists.
The next three pictures combine reality. The game is throwing hexahedral dice. The basic rules are: throw 50% of the lost capital, throw at 6 points to get 50% profit of the principal amount, and the remaining points 5% of the profit principal. It was thrown a total of 300 times, first the original path cloud, followed by two path clouds that superimposed safe haven strategies — value storage and insurance, respectively.
Let's summarize the characteristics of the above three graphs: First, the original distribution map is the broadest, with an arithmetic average yield of 3.3%. This is the highest because the large number of the few optimal paths contributes greatly to the calculation of the arithmetic average; on the other hand, its geometric average yield is -1.5%, which is also the lowest. This also causes the distance between the two to the largest of the three charts. The size of this distance can be compared to the level of fluctuation. The farther the distance, the greater the fluctuation, the higher the invisible and huge “fluctuation tax” imposed by the market. We accept the geometric average return because it is consistent with reality: after 300 throws, wealth changes from 1 to 0.001 (left side benchmark).
Second, after adopting the safe haven strategy, the distribution map was deformed and displaced. The value storage strategy in the second chart morphed the graph: from a normal distribution to a peak fat tail distribution. This distribution significantly reduced the gap between the arithmetic average yield of 1.3% and the geometric average yield of 0.6%. According to the analogy in the previous section, the fluctuation became smaller. In reality, it is equivalent to using the Kelly formula to play games. If the distance changes to an extreme value of 0, what does that mean? This is the traversal state. At this point, the arithmetic average yield is the geometric average yield, and the real world will become a parallel universe.
Finally, the insurance strategy in the third chart goes one step further. Not only is the peak fat end distribution, but the entire distribution has moved upward. This has caused the actual geometric average yield to continue to rise. The arithmetic average yield is 3.0%, and the geometric average yield is 2.1%. This is simply amazing. Compared to the original distribution, it not only raised the high digits, but the entire path cloud — all quantile paths went one level overall, which meant we had no regrets no matter what.
If this is a mechanical law (which is always the case), unaffected by statistical factors (a trend formed over time), it means we are close to being the best. So is this a rule? At least we can't falsify this in terms of time. The reason is that the simulated occurrence and one-by-one verification principle we mentioned earlier is the simulation of full-path data, which of course includes a simulation of the future. Therefore, under the entire sample data, the sampling does not only follow the survivor's path, but also includes evidence of poor silence in reality. It uses a holistic view to overcome the effects of time factors. The extent to which this conclusion can be confirmed is logically as clear as Wu Woo 2, but this is still not all of our standards.
These images are also inspired by Nietzsche's ideas. My understanding is that when Nietzsche says N=1, the path we will eventually experience is only one; when Nietzsche talks about eternal reincarnation, it means that we all continuously cycle in the game's original path cloud distribution pattern or in all path clouds between applying additional two different strategies (various alpha strategies); when Nietzsche says that we love your life, it means that it is possible for us to find the best.
Let's lay the right side of the three maps flat and stack them under the same horizontal coordinates to form a new map. Here we need to break down inherent perceptions and reveal the most hidden part — how to view costs and benefits, which I want to explain in detail.
It seems that we have always regarded explicit cost as an initial condition to measure the final rate of return, in order to be able to implement this established expected path in the future, but it seems that reality has never verified that there is such a match, and the actual final return only requires two equity values at the beginning and end of the period, so this kind of calculation procedure seems unnecessary.
It also causes our tendency to think linearly, that is, the apparent cost of compression will eventually be reflected in equal proportions in the final benefit. Of course, cost savings help generate net benefits; the problem lies in the hidden perception of “equal proportions”. Logically, the safe haven strategy we adopted is to hedge against tail risk by using a kind of profit surging at the tail end. Of course, this is a non-linear, exponential increase. This is a completely different category of things from linear thinking in equal proportions. Its small apparent cost is a relative cost, and it is all used to obtain a large amount of excess relative return during the collapse period. This is like a safe haven strategy that has the magic effect of pulling a larger rabbit out of a magic hat with a lower brim.
The purpose of cost calculation is mainly to construct our final evaluation criteria — a cost-benefit analysis chart. Our overall goal will always be the geometric average return, but cost can also be an important part of the final evaluation criteria of cost-benefit analysis. As an examination framework, cost is not simply an explicit cost, but rather a relative change in the overall cost after applying or not applying a strategy. The calculation process is also reversed, comparing the overall cost (relative cost) of “savings” obtained from the difference between applying a safe haven strategy and the arithmetic average rate of return (no strategy applied).
The overall cost is composed of explicit costs and hidden costs. Implicit costs are also known as opportunity costs. Compared to straightforward explicit costs, hidden hidden costs are difficult to reveal. Some people can completely ignore hidden costs. This is ignoring opportunity costs — a fatal hidden bias. The geometric average return is a compound time dimension, and the arithmetic average return related to cost does not cover the dimension of time. It is clearly a low-dimensional indicator. Therefore, the forward estimation process from cost to benefit can not only be accurately expressed because hidden costs are difficult to portray, but also cannot directly match the actual geometric average rate of return.
In describing the concepts of cost, arithmetic average rate of return, and geometric average return, we have always firmly fixed the overall goal of geometric average return. Nietzsche said, “Forgetting one's purpose is the most common foolish act,” which requires us to establish an overall concept. Aristotle said this in his book “Metaphysics”: The whole is not the accumulation of parts, but something outside of parts. When classifying things, his focus is not on the basic properties that are out of place, but on how those attributes and parts interact with the environment. Essence refers to the degree to which an organism functions and develops successfully in the environment.
In order not to make the above expressions difficult to understand because they are abstract, here are two specific examples:
In the case of a cuckoo clock, if you take it apart and lay all the parts flat on the table, then many of its interacting parts are independent and separate. The sum of this bunch of parts doesn't have much value, but once assembled by craftsmen, it creates a “weak emergence” phenomenon: the interaction of the parts does not change each other, but creates characteristics that can only be observed in the whole.
Similarly, in a game of throwing dice, bets using Kelly or insurance bets have overall attributes that cannot be obtained by accumulating a single bet. The rebalancing and compounding effects of a single bet are constantly iterated, and the overall attributes come from this interaction. The reason the safe haven strategy dramatically increases end-of-period wealth is due to the iterative nature of the game. Each time the roll ends, the size of the bet is reset or rebalanced to fund the next roll. These bets are no longer isolated from each other, act alone, but interact. As a result, a brand new whole was formed, a whole very different from the sum of its parts. This is called a “strong emergence.”
If we can actually understand and agree with the above overall idea, we will surely seriously and resolutely oppose the traditional partial idea: the whole is the sum of the parts. The impact of this misthinking is almost deep-rooted and ubiquitous. For example, the idea that as long as you achieve the best in every step of the work, then the overall plan or path is optimal. The truth is that in order to achieve overall excellence, not only can parts be sacrificed, but must be sacrificed.
Once you've sorted out these basic concepts, it's easy to understand the above composite chart. From top to bottom, from not applying a safe haven strategy to a value storage strategy (Kelly bet) to an insurance strategy, the median (geometric average return) continues to move to the right, while the net effect of the portfolio (the difference in geometric average return) continues to expand positively; at the same time, the arithmetic cost of this process is decreasing. Reduced arithmetic costs combined with a larger net portfolio effect. This dual effect is known as an economic advantage strategy.
Investment relativity stipulates that the value of an investment can only be determined by the net effect of the portfolio it produces, so it is unique and relative to that (and others) specific investment portfolio. The whole is often (but not always) far greater than the sum of its parts.
Results of calculation guesses
Investment games are the same type of thing as throwing hexahedral dice, except that the former uses 120-sided dice, which correspond to the 120 annual returns of the S&P 500 from 1900 to 2020. Through random throwing, 25 yields are selected to cover the 25-year period of Monte Carlo simulation, and this process is repeated 10,000 times to form a path cloud, and the profit range is increased from 3 to 5.
The first layer yield distribution chart below is consistent, and the geometric average yield in the second layer chart is also consistent. The geometric average yield calculation method is calculated by multiplying the medians of each interval, and the arithmetic average return and geometric average return are labeled in the self-service method column. The returns of three different additional strategies are listed in the third level. The alpha strategy is a strategy between value storage and insurance strategies. In the self-service method column, the arithmetic average yield of value storage and alpha is set at 7%, and the insurance strategy is 0. When two- and three-layer maps are combined, a fourth level chart is generated. In the self-service method column, only the insurance strategy obtains a net effect of 0.5%.
Of course, this 0.5% net effect is not a product of the certification law; it is generated during the falsification process. Our null hypothesis (antecedent, full statement) is: “A strategy can cost-effectively reduce portfolio risk.” Our goal is to falsify this hypothesis based on deductive reasoning that negates the aftermath (statement alone), and this can be done by negating the conditional premise that adding this strategy will increase the compound annual growth rate of the portfolio over time. If this premise is denied, then the null hypothesis is denied. Obviously, the insurance strategy won out. However, value storage and alpha strategies have failed the test of falsification; their net effect is negative, so they are safe haven counterfeit products.
I also want to reveal why an economical advantage strategy such as insurance doesn't get people's attention? First, the number of Bernoulli Falls-level falls as shown in the first layer chart itself (first bar chart) is very small, and all of our relative returns occur here. Relative yield refers to the difference between the absolute return 0 of the first composite coordinate point in the third column and the original collapse yield. The improvement it received was the greatest, just like winning in defeat, and all of this is due to the existence of an insurance value of 10 times the insurance value corresponding to the first coordinate point in the third column of the third layer chart, but most notable people only pay attention to the absolute return rate in the positive direction; secondly, in the end What The average yield is calculated by multiplying the yields. After being hidden twice, the difference between it and other strategies is almost inconspicuous.
What would happen if the collapse didn't happen in reality? The results after verification in the following figure are as follows. The geometric average return under the three safe haven strategies had little effect. Some people will question that its net benefit is -2.3%, which is still false compared to the index benchmark? However, this index benchmark is only an assumption, not reality. These are two completely different things. It is like asserting that the market will never plummet. The truth is: in reality, there will always be black swans, so it is impossible to compare them in this way.
I've been looking for where is the real mistake in our thinking? As far as the safe haven issue is concerned, one potential misconception is that when the starting point equals the end point, buying insurance is paying for nothing. It's ridiculous or not! Because what we have been trying to overcome is huge losses caused by high, invisible fluctuations, the safe haven strategy is related to volatility. As long as there is fluctuation, there is a chance to win. The greater the fluctuation, the greater the profit, and one of the essential properties of the market is fluctuation.
We included the numbers on the self-help method scoreboard into our final evaluation criteria. The horizontal coordinate is the arithmetic cost savings, the vertical coordinate is the net effect, the slash in the first quadrant is the S&P 500 baseline, and the upper left blank area is the acceptance area. This means getting more net effects at lower arithmetic costs — an economical advantage strategy, and the lower right shaded area is the rejection area.
About restructuring. We're re-creating a self-help experiment. Create a 25-year path by rolling the d120 dice to obtain 25 S&P 500 yields and 25 safe haven yields, and randomly reorganize the order in which these returns occurred. To be clear, we still have the 25 S&P 500 yields and 25 safe haven yields that the d120 dice originally threw, but now they are random combinations rather than adjusted based on safe haven yields. This means that the yield and frequency of each risk-mitigated portfolio remains the same, but the specific year of each yield is no longer tied to the S&P 500 yield. The results are as follows: The cost-effect floor plan after random restructuring shows that it falls back into the rejection zone, so we must implement insurance strategies that match risk.
The question of configuration ratios is a key one. The sensitivity of safe havens to revenue distortions is often more important than the shape of earnings themselves. Sensitivity is the main dividing line between safe havens and counterfeit safe havens. Other strategies include the Kelly bet (value storage) pictured on the left. The median is different from the 5% quantile cash allocation ratio, which is why professional gamblers bet between 10% and 40% of the principal amount. If the left image is compressed, or the horizontal scale of the right image is adjusted (for example, using 10,000 points to mark the ratio ratio, which is equivalent to stretching), then the left image and the right image actually have the same shape. Therefore, the horizontal coordinates of the median fraction and the 5% quantile are actually always different. However, once compressed, sensitivity immediately takes effect. In reality, it has been observed that the ratio accuracy of paths with different quantiles can be raised to a level within 1 thousandth point. As a result, insurance strategies can complete the protective effect with a very low allocation ratio, silently integrating assets like salt, and fully covering everything from the worst path through the median path to the optimal path to risk hedging. This is also known as the Golden Girl principle. There are no more, no less, and just right.
Direct comparison of calculation results with observations
The last step is to simply repeat the above process to enter the cost effect plan of all the realistic safe havens — short-term treasury bonds, long-term treasury bonds, commodities, gold, etc., one generation at a time. We can draw a line intersecting the three cartoon safe haven prototypes on the map and extend this line in two directions. Obviously, this line is significant; it is called the safe haven boundary line. In reality, gold falls into the acceptance zone, and 20-year treasury bonds are also very close, but they all have statistical factors (proven reasons include base difference risk, inflation risk, safe investment transfer effect, counterparty risk), and I won't go into detail here. Insurance strategies maximize returns without using luck.
At this point, let's summarize the advantages and disadvantages of insurance havens. The advantages are: 1. As long as the funds are sustainable in time, they will surpass the benchmark; 2. For fluctuations in the process, it can also prevent situations where you have to trade during the crash; 3. We have also obtained a valuable option. It is brought about by the difference between the simulated operation data points and the actual fluctuation range. Within the range, as long as there is a sharp drop at the level of Bernoulli Falls, you can choose to fix the position at any time below the collapse level by cashing out a two-way or one-way position This part or all The relative return is equivalent to winning by increasing the probability, which a bullish strategy will never be able to achieve. The value of this alternative cannot be measured in detail; it depends on how it was specifically operated at the time. The downside of the safe haven strategy is that you will have to face the pain of falling slightly behind the benchmark for a long time. In the simulation test, there is only a 11/120 time probability of generating sharp returns. Although in practice, the above options can help us increase our probability a bit, but we have always paid small insurance premiums for other long periods of time. This does require sufficient strength to maintain faith. I believe it is a strategy to win in the end. Offense wins the game, and defense wins the championship.
Finally, I would like to emphasize my idea: as I understand it, a theory that has not been falsified until now may one day be falsified, but to the extent that it can be confirmed, it is clearly more promising than various theories that have already been falsified, because if it is wrong, there is still a chance for the right one. Both science and investment are made up of theories or essays that have not yet been rejected, and their history is the tomb of rejected theories and papers. As a result, it became my current belief. The purpose of this best effort to prove falsification is simply to maintain (live) in the complex system of the investment sector; it is by no means for high returns (chasing high returns is a fake problem; the second paragraph of this article already uses the fallacy method to explain that there is no magic crystal ball), and I also firmly believe in this simple and unbreakable truth: the ultimate winner can only be born from competitors that remain in existence.
Editor/Jeffrey